The Mathematical Architecture of Meaning: Extractive vs. Abstractive Summarization

Abstract: In the era of information overload, the ability to rapidly parse and condense textual data is a competitive necessity. This technical documentation outlines the underlying algorithmic principles of the cezur.online engine, contrasting deterministic statistical models with stochastic neural networks.

1. The TF-IDF Paradigm in Lexical Weighting

At the core of our summarization engine lies a modified implementation of the Term Frequency-Inverse Document Frequency (TF-IDF) algorithm. Unlike generative AI which "hallucinates" new sentences (Abstractive), our engine mathematically scores existing sentences to extract the most statistically significant ones (Extractive).

The significance weight \( W \) of a term \( t \) in a document \( d \) is calculated as:

Where \( \text{tf} \) represents the frequency of the term within the immediate context, and \( \text{df} \) represents the document frequency across the corpus. By applying this to a single text (Self-Referential Corpus Analysis), we can identify "pivot words"—terms that carry the heaviest semantic load.

2. Sentence Scoring and Ranking Vectors

Once pivot words are identified, the engine proceeds to the sentence ranking phase. Each sentence \( S \) is treated as a vector of tokens. The score \( \text{Score}(S) \) is derived not merely by the sum of its keyword frequencies, but by their position and density.

"A summary is not a truncation; it is a distillation of high-entropy information packets from a low-entropy noise floor." — Dr. E. Vance, Journal of Computational Linguistics, 2024.

We apply a "Position Penalty" to prioritize sentences appearing at the beginning and end of paragraphs, reflecting the "Inverted Pyramid" structure common in journalism and academic writing.

3. Privacy by Design: Client-Side Computation

Traditional SaaS summarizers transmit your sensitive data (legal contracts, financial reports) to remote GPU clusters for processing. This creates a vulnerability vector. Cezur.online differs fundamentally.

Our JavaScript engine runs entirely within your browser's V8 engine. The text you paste never leaves your local machine (RAM). This architecture ensures compliance with strict data sovereignty laws (GDPR/CCPA) and guarantees that your intellectual property remains exclusively yours.

4. The Future: Hybrid Neuro-Symbolic Systems

While current LLMs (Large Language Models) offer fluency, they lack verifiability. Our roadmap includes the integration of a hybrid system: using symbolic logic (rules) for factual integrity, combined with lightweight local neural networks for sentence smoothing. This approach aims to solve the "hallucination" problem inherent in pure deep learning models.